We consider a group of m+1 trusted nodes that aim to create a shared secret key K over a network in the presence of a passive eavesdropper, Eve. We assume a linear non-coherent network coding broadcast channel (over a finite field F_q) from one of the honest nodes (i.e., Alice) to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free public channel which is also overheard by Eve.
For this setup, we propose upper and lower bounds for the secret key generation capacity assuming that the field size q is very large. For the case of two trusted terminals (m = 1) our upper and lower bounds match and we have complete characterization for the secrecy capacity in the large field size regime.
We consider perfect secret key generation for a ``pairwise independent network'' model in which every pair of terminals share a random binary string, with the strings shared by distinct terminal pairs being mutually independent. The terminals are then allowed to communicate interactively over a public noiseless channel of unlimited capacity. All the terminals as well as an eavesdropper observe this communication. The objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible, and concealed from the eavesdropper. First, we show how the notion o…
A key agreement problem is considered that has a biometric or physical identifier, a terminal for key enrollment, and a terminal for reconstruction. A nested convolutional code design is proposed that performs vector quantization during enrollment and error control during reconstruction. Physical identifiers with small bit error probability illustrate the gains of the design. One variant of the nested convolutional codes improves on the best known key vs. storage rate ratio but it has high complexity. A second variant with lower complexity performs similar to nested polar codes. The results su…
Hypergraphical sources are a natural class of sources for secret key generation, within which different subsets of terminals sharing secrets are allowed to discuss publicly in order to agree upon a global secret key. While their secrecy capacity, i.e., the maximum rate of a secret key that can be agreed upon by the entire set of terminals, is well-understood, what remains open is the maximum rate of a secret key that can be generated when there is a restriction on the overall rate of public discussion allowed. In this work, we obtain a family of explicitly computable upper bounds on the number…
In this paper, we consider a more general four-terminal memoryless relay-eavesdropper channel with state information (REC-SI) and derive an achievable perfect secrecy rate for it. We suppose that the state information is non-causally available at the transmitter and relay only. The transmitter wishes to establish a secure communication with the legitimate receiver by the help of a relay where a confidential message will be kept secret from a passive eavesdropper. We consider active cooperation between the relay and transmitter. The relay helps the transmitter by relaying the message using deco…
In this paper, we consider the standard discrete-time slotted ALOHA with a finite number of terminals with infinite size buffers. In our study, we jointly consider the stability of this system together with the physical layer security. We conduct our studies on both dominant and original systems, where in a dominant system each terminal always has a packet in its buffer unlike in the original system. For N = 2, we obtain the secrecy-stability regions for both dominant and original systems. Furthermore, we obtain the transmission probabilities, which optimize system throughput. Lastly, this pap…
A two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices at the legitimate terminals are fixed and revealed to all the terminals, whereas the channel matrix of the eavesdropper is arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver and uses a single-user wiretap code is shown to be sufficient to achieve t…
We consider a model for secrecy generation, with three terminals, by means of public interterminal communication, and examine the problem of characterizing all the rates at which all three terminals can generate a ``secret key,'' and -- simultaneously -- two designated terminals can generate a ``private key'' which is effectively concealed from the remaining terminal; both keys are also concealed from an eavesdropper that observes the public communication. Inner and outer bounds for the ``secret key--private key capacity region'' are derived. Under a certain special condition, these bounds coi…
This paper considers satellite eavesdroppers in uplink satellite communication systems where the eavesdroppers are randomly distributed at arbitrary altitudes according to homogeneous binomial point processes and attempt to overhear signals that a ground terminal transmits to a serving satellite. Non-colluding eavesdropping satellites are assumed, i.e., they do not cooperate with each other, so that their received signals are not combined but are decoded individually. Directional beamforming with two types of antennas: fixed- and steerable-beam antennas, is adopted at the eavesdropping satelli…
The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of the key-leakage-storage regions of the generated-secret and chosen-secret models. The second construction uses nested polar codes for vector quantization during enrollment and for error correction during reconstruction. Simulations show that the nested polar codes achieve privacy-leakage and storage rates that improve on existing code designs. One proposed co…
This work is motivated by recent results of Csiszar and Narayan (IEEE Trans. on Inform. Theory, Dec. 2004), which highlight innate connections between secrecy generation by multiple terminals and multiterminal Slepian-Wolf near-lossless data compression (sans secrecy restrictions). We propose a new approach for constructing secret and private keys based on the long-known Slepian-Wolf code for sources connected by a virtual additive noise channel, due to Wyner (IEEE Trans. on Inform. Theory, Jan. 1974). Explicit procedures for such constructions, and their substantiation, are provided.
The key-leakage-storage region is derived for a generalization of a classic two-terminal key agreement model. The additions to the model are that the encoder observes a hidden, or noisy, version of the identifier, and that the encoder and decoder can perform multiple measurements. To illustrate the behavior of the region, the theory is applied to binary identifiers and noise modeled via binary symmetric channels. In particular, the key-leakage-storage region is simplified by applying Mrs. Gerber's lemma twice in different directions to a Markov chain. The growth in the region as the number of …
Interference in wireless networks degrades the signal quality at the terminals. However, it can potentially enhance the secrecy rate. This paper investigates the secrecy rate in a two-user interference network where one of the users, namely user 1, requires to establish a confidential connection. User 1 wants to prevent an unintended user of the network to decode its transmission. User 1 has to transmit such that its secrecy rate is maximized while the quality of service at the destination of the other user, user 2, is satisfied, and both user's power limits are taken into account. We consider…
We consider two fundamental multi-user channel models: the multiple-input multiple-output (MIMO) wiretap channel with one helper (WTH) and the MIMO multiple access wiretap channel (MAC-WT). In each case, the eavesdropper has $K$ antennas while the remaining terminals have $N$ antennas each. We consider a fast fading channel where the channel state information (CSI) of the legitimate receiver is available at the transmitters but no channel state information at the transmitters (CSIT) is available for the eavesdropper's channel. We determine the optimal sum secure degrees of freedom (s.d.o.f.) f…
We consider secret key generation for a "pairwise independent network" model in which every pair of terminals observes correlated sources that are independent of sources observed by all other pairs of terminals. The terminals are then allowed to communicate publicly with all such communication being observed by all the terminals. The objective is to generate a secret key shared by a given subset of terminals at the largest rate possible, with the cooperation of any remaining terminals. Secrecy is required from an eavesdropper that has access to the public interterminal communication. A (single…
We propose a method to study the secrecy constraints in key generation problems where side information might be present at untrusted users. Our method is inspired by a recent work of Hayashi and Tan who used the Rényi divergence as the secrecy measure to study the output statistics of applying hash functions to a random sequence. By generalizing the achievability result of Hayashi and Tan to the multi-terminal case, we obtain the output statistics of applying hash functions to multiple random sequences, which turn out to be an important tool in the achievability proof of strong secrecy capacit…
We study the fundamental limits to secret key generation from an excited distributed source (EDS). In an EDS a pair of terminals observe dependent sources of randomness excited by a pre-arranged signal. We first determine the secret key capacity for such systems with one-way public messaging. We then characterize a tradeoff between the secret key rate and exponential bounds on the probability of key agreement failure and on the secrecy of the key generated. We find that there is a fundamental tradeoff between reliability and secrecy. We then explore this framework within the context of recipro…
In future practical deployments of massive multi-input multi-output (MIMO) systems, the number of radio frequency (RF) chains at the base stations (BSs) may be much smaller than the number of BS antennas to reduce the overall expenditure. In this paper, we propose a novel design framework for joint data and artificial noise (AN) precoding in a multiuser massive MIMO system with limited number of RF chains, which improves the wireless security performance. With imperfect channel state information (CSI), we analytically derive an achievable lower bound on the ergodic secrecy rate of any mobile t…
A subset of a set of terminals that observe correlated signals seek to compute a given function of the signals using public communication. It is required that the value of the function be kept secret from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the "aided secret key" capacity of an associated secrecy generation model, for which a single-letter characterization is provided.
In this paper, we consider secure downlink transmission in a multi-cell massive multiple-input multiple-output (MIMO) system where the numbers of base station (BS) antennas, mobile terminals, and eavesdropper antennas are asymptotically large. The channel state information of the eavesdropper is assumed to be unavailable at the BS and hence, linear precoding of data and artificial noise (AN) are employed for secrecy enhancement. Four different data precoders (i.e., selfish zero-forcing (ZF)/regularized channel inversion (RCI) and collaborative ZF/RCI precoders) and three different AN precoders…
We propose an approach for constructing secret and private keys based on the long-known Slepian-Wolf code, due to Wyner, for correlated sources connected by a virtual additive noise channel. Our work is motivated by results of Csiszár and Narayan which highlight innate connections between secrecy generation by multiple terminals that observe correlated source signals and Slepian-Wolf near-lossless data compression. Explicit procedures for such constructions and their substantiation are provided. The performance of low density parity check channel codes in devising a new class of secret keys is…
University of Siegen（锡根大学）；Linköping University（林雪平大学）；Technical University of Munich（慕尼黑工业大学）；Ruhr-Universität Bochum（波鸿鲁尔大学）；Princeton University（普林斯顿大学）
The problem of secure source coding with multiple terminals is extended by considering a remote source whose noisy measurements are the correlated random variables used for secure source reconstruction. The main additions to the problem include 1) all terminals noncausally observe a noisy measurement of the remote source; 2) a private key is available to all legitimate terminals; 3) the public communication link between the encoder and decoder is rate-limited; and 4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured w…
